Phase diagram. We illustrate the \(\rho -T\)  phase diagram for classroom movement in Figure 3d. For temperature below the critical temperature \(T_c\) , the system undergoes a vapor-liquid phase transition where different phases are governed by the system density. The low-density regime (\(\rho <\rho _v\) ) corresponds to a vapor phase, whereas the high-density regime (\(\rho >\rho _l\) ) represents a liquid. When density is between \(\rho _v\)  and \(\rho _l\) , vapor and liquid coexist. The density difference \(\Delta \rho =\rho _l-\rho _v\sim (T_c-T)^{\beta }\)  decreases as temperature \(T\)  approaches \(T_c\) , where the critical exponent \(\beta =1/2\)  for mean field theory [1]} and \(\beta \approx 0.35\pm 0.15\)  experimentally for molecules [2]}, [3]}. The distinction between vapor and liquid disappears when \(T = T_c\) , and above \(T_c\)  the system is gas-like.
